You Do Need power plug adapter while traveling from Oman to Dominica.

Here is Why You Need An Adapter

The outlet and plug type used in Dominica are D and G and in Oman is G. This is how they look like.

Oman

In Oman, outlets of type G are in use.

Type G

Dominica

In Dominica, outlets of type D and G are in use.

Type D

Type G